Multipolar interactions play a pivotal role in governing emergent phenomena in quantum materials, including multiferroics and quantum magnetism. In this work, we determine the ground-state phase diagram of the nearest-neighbor spin-$\frac{3}{2}$ bilinear-biquadratic-bicubic Heisenberg model on the square lattice through a combination of mean-field theory and exact diagonalization. We demonstrate that quantum fluctuations can drive the emergence of multisublattice ordered phases, even on a bipartite lattice, provided that multipolar interactions are sufficiently strong. To characterize the excitation spectra across these distinct phases, we develop cluster spin-wave theory—an extension of conventional linear spin-wave theory—which enables the reliable description of both low-energy magnon dispersions and high-energy multimagnon continua. Our findings offer valuable insights into the nature of collective excitations in strongly correlated spin systems and establish a robust theoretical framework for understanding spin dynamics in complex quantum magnets.

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• Frustrated magnetism
• 2-dimensional systems
• Magnetic systems
• Strongly correlated systems
• Exact diagonalization
• Linear spin wave theory
• Mean field theory